EuPtSi: Chiral Magnetism & Topological Phases

• EuPtSi is a chiral intermetallic antiferromagnet with a trillium lattice and Dzyaloshinskii–Moriya interactions that drive complex magnetic orders.
• Its low-temperature phase exhibits single-chirality helical order that transitions into a field-induced triangular skyrmion lattice with nanometric periodicity.
• The compound also supports topological phononic and electronic surface modes arising from its noncentrosymmetric cubic symmetry.

Searching arXiv for recent EuPtSi papers and core references. EuPtSi is a cubic chiral intermetallic antiferromagnet in space group $P2_13$ (No. 198), with Eu ions forming a trillium lattice, a three-dimensional network of corner-sharing equilateral triangles. Its low-temperature physics combines localized Eu$^{2+}$ moments with metallic conduction, noncentrosymmetric exchange couplings, and pronounced magnetic frustration. As a result, EuPtSi has become a reference system for short-period helical order, multiple-$Q$ magnetism, and a field-induced triangular skyrmion lattice, while more recent work has also identified chiral phononic and electronic surface modes tied to the same crystal symmetry (Kaneko et al., 2018, Mahraj et al., 2024, Khatua et al., 27 Nov 2025).

1. Crystal structure and materials identity

EuPtSi crystallizes in the chiral cubic space group $P2_13$, with lattice constant $a = 6.433~\mathrm{\AA}$ and Eu–Eu distance $3.94~\mathrm{\AA}$. The magnetic ion is Eu$^{2+}$ with $S=7/2$ and $L=0$. The trillium lattice realized by the Eu sublattice is geometrically frustrated and, because the structure lacks inversion symmetry, it permits antisymmetric exchange in the form of the Dzyaloshinskii–Moriya interaction (DMI) (Khatua et al., 27 Nov 2025).

EuPtSi is metallic: conduction electrons mediate RKKY interactions between localized Eu $4f$ moments. This combination of RKKY exchange, DMI, and frustration is central to the compound’s magnetic phase diagram and to its short magnetic modulation period relative to canonical chiral magnets such as MnSi (Hayami et al., 2021, Khatua et al., 27 Nov 2025).

EuPtSi should be distinguished from EuPtSi$^{2+}$0. The latter is a noncentrosymmetric tetragonal antiferromagnet in space group $^{2+}$1 and exhibits a different hierarchy of magnetic transitions and long-wavelength antiferromagnetic cycloids rather than the cubic trillium-lattice physics of EuPtSi (Bauer et al., 2022).

2. Zero-field order and chiral helimagnetism

EuPtSi orders antiferromagnetically at $^{2+}$2 in neutron diffraction measurements, while transport work reports $^{2+}$3 K. In the ground state at $^{2+}$4 K, single-crystal neutron diffraction finds magnetic peaks at

$^{2+}$5

and its cyclic permutations. Upon heating, an additional magnetic peak splitting appears around $^{2+}$6, indicating a first-order commensurate-incommensurate transition to

$^{2+}$7

with $^{2+}$8 and clear hysteresis between warming and cooling (Kaneko et al., 2018).

Half-polarized neutron scattering establishes that the helical order has a single chiral character and that the ordered moments lie perpendicular to the ordering vector. The relevant polarization dependence is

$^{2+}$9

with the cross term encoding helicity. Experimentally, the channel with neutron spin antiparallel to the scattering vector is stronger in both the ground state and the intermediate phase, which identifies a single-chirality helical structure (Kaneko et al., 2018).

At higher temperatures, EuPtSi shows a positive Curie–Weiss temperature $Q$0, critical slowing down of Eu$Q$1 spin fluctuations above and at $Q$2, and only $Q$3 entropy release at $Q$4. These observations indicate that substantial magnetic correlations persist above the onset of long-range order (Khatua et al., 27 Nov 2025).

3. Field-induced skyrmion lattice

For magnetic field along $Q$5, EuPtSi exhibits a field-induced A-phase. Neutron diffraction at $Q$6 T and $Q$7 K shows that magnetic Bragg peaks move into the plane perpendicular to the field and form hexagonal patterns around nuclear Bragg points. The corresponding modulation vector is

$Q$8

with nearly the same periodic length as $Q$9 but reoriented perpendicular to the field. This hexagonal superlattice was interpreted as the hallmark of skyrmion-lattice formation in EuPtSi (Kaneko et al., 2018).

Resonant x-ray diffraction later resolved the A-phase as a triple-$P2_13$0 triangular skyrmion lattice for $P2_13$1, with propagation vectors

$P2_13$2

where approximately $P2_13$3, $P2_13$4, and $P2_13$5. All three Fourier components are perpendicular to their respective $P2_13$6 vectors and have the same helicity; they are related by rotations about the $P2_13$7 axis. The helicity matches that of the low-field single-$P2_13$8 helimagnetic phase, indicating that the antisymmetric exchange interaction inherent in the chiral structure supports the triangular skyrmion lattice (Matsumura et al., 2024).

The field evolution is not a direct helix-to-skyrmion conversion. Just below the first-order transition to the skyrmion lattice, the helical plane tilts toward the magnetic field to form a conical structure; at $P2_13$9 T the tilt angle is about $a = 6.433~\mathrm{\AA}$0. In the A-phase, the real-space texture has a periodicity of $a = 6.433~\mathrm{\AA}$1, placing EuPtSi in the regime of nanometric skyrmion crystals (Matsumura et al., 2024).

4. Microscopic models and stabilization mechanisms

A symmetry-based description of EuPtSi follows from the classification of momentum-dependent anisotropic exchange interactions in cubic systems. For the noncentrosymmetric cubic groups $a = 6.433~\mathrm{\AA}$2, $a = 6.433~\mathrm{\AA}$3, and $a = 6.433~\mathrm{\AA}$4, the allowed interactions include both symmetric anisotropic exchange and Dzyaloshinskii–Moriya terms. EuPtSi crystallizes in $a = 6.433~\mathrm{\AA}$5, which is isomorphic to $a = 6.433~\mathrm{\AA}$6, so the relevant interaction matrix can contain triaxial symmetric anisotropy, off-diagonal symmetric terms, and two independent DM components. For a $a = 6.433~\mathrm{\AA}$7-type wave vector, one allowed form is

$a = 6.433~\mathrm{\AA}$8

with cyclic counterparts for symmetry-related $a = 6.433~\mathrm{\AA}$9 vectors (Yambe et al., 2023).

Within this framework, momentum-dependent anisotropy is the origin of multiple-$3.94~\mathrm{\AA}$0 instabilities. It can select competing symmetry-related $3.94~\mathrm{\AA}$1 vectors, favor superpositions of more than one spin density wave, and, with DM terms, stabilize chiral textures. The resulting states include double-$3.94~\mathrm{\AA}$2 structures, triple-$3.94~\mathrm{\AA}$3 structures, hedgehog-antihedgehog cubic lattices, and skyrmion lattices. The discussion in this context explicitly identifies EuPtSi as an example of a noncentrosymmetric magnet whose observed multiple-$3.94~\mathrm{\AA}$4 states can be understood in terms of symmetry-allowed anisotropic exchange (Yambe et al., 2023).

A complementary minimal effective spin model for EuPtSi is

$3.94~\mathrm{\AA}$5

Here $3.94~\mathrm{\AA}$6 is an RKKY-type bilinear exchange, $3.94~\mathrm{\AA}$7 is a biquadratic multiple-spin interaction from itinerant electrons, and $3.94~\mathrm{\AA}$8 represents long-range DM coupling. The model identifies two key ingredients for EuPtSi-like nanometric skyrmion crystals: low-symmetric ordering vectors and the synergy between spin-charge and spin-orbit couplings. For $3.94~\mathrm{\AA}$9 fields, skyrmion crystals are stabilized by the DM interaction over a wide parameter range, even for small or vanishing $^{2+}$0, whereas for $^{2+}$1 and $^{2+}$2 fields the stability requires nonzero $^{2+}$3 (Hayami et al., 2021).

5. Transport signatures and metastability

Transport measurements resolve strong orientation dependence below $^{2+}$4 K. For $^{2+}$5, the thermodynamically stable skyrmion-lattice A-phase occurs inside the conical phase between $^{2+}$6 K and $^{2+}$7 in the field range from $^{2+}$8 T to $^{2+}$9 T. Its transport signatures include a resistivity bump with a maximum additional scattering $S=7/2$0 at $S=7/2$1 K and a positive topological Hall effect (THE) peak between the critical fields $S=7/2$2 and $S=7/2$3; the magnitude of the THE signal is around $S=7/2$4 (Rousseau et al., 7 Oct 2025).

The same study shows that the A-phase is remarkably metastable. After field cooling through the equilibrium A-phase regime, the skyrmion-lattice state persists down to the lowest measured temperatures, $S=7/2$5 K, regardless of cooling rate or magnetic history, and remains stable for at least $S=7/2$6 hours. Field sweeps below $S=7/2$7 K reveal strong hysteresis, consistent with the first-order character of the A-phase boundaries and with well-separated free-energy minima (Rousseau et al., 7 Oct 2025).

For $S=7/2$8, two additional topological phases are observed within the conical background: an A$S=7/2$9-phase between $L=0$0 and $L=0$1 and a B-phase between $L=0$2 and $L=0$3. Both produce anomalous increases in resistivity and clear, though smaller, topological Hall signals; both can also be stabilized metastably far below their equilibrium temperature range by field cooling. No exotic phases are detected for $L=0$4. The precise real-space configurations of the A$L=0$5- and B-phases are not yet resolved, but their Hall anomalies indicate nontrivial scalar spin chirality (Rousseau et al., 7 Oct 2025).

6. Electronic and phononic topology

Beyond its magnetic phase diagram, EuPtSi has been studied as a chiral topological crystal with bulk and surface band topology rooted in $L=0$6 symmetry. First-principles calculations find, for phonons, a spin-1 Weyl point at $L=0$7 and a charge-2 Dirac point at $L=0$8, with corresponding Chern numbers $L=0$9 and $4f$0. In the electronic structure, the same spin-1 Weyl and charge-2 Dirac features appear at $4f$1 and $4f$2 in the absence of spin–orbit coupling; with spin–orbit coupling, the $4f$3 node splits into a doubly degenerate point with $4f$4 and a fourfold degenerate state, while the $4f$5 node decouples into a sixfold fermionic point with $4f$6 and a doubly degenerate trivial point (Mahraj et al., 2024).

These bulk nodes generate chiral surface states. On the $4f$7 surface, both phononic and electronic spectra exhibit chiral edge modes connecting the surface projections $4f$8 and $4f$9. The chiral phononic edge mode is associated with the vibration of atoms in close vicinity, whereas the chiral electronic surface states correspond to carrier accumulation at the edge of chiral atomic chains. In the electronic case, the surface manifestations are Fermi arcs whose number tracks the absolute value of the relevant Chern number (Mahraj et al., 2024).

Taken together with the real-space magnetic topology of the A-phase, these results place EuPtSi at the intersection of chiral magnetism, frustrated metallic exchange, and symmetry-protected band topology. A plausible implication is that EuPtSi provides a single material platform in which skyrmion-lattice physics and chiral phononic or electronic boundary modes can be examined concurrently.